In gas turbines, the rotor, the inner part of rotor discs, sealing members on the rotor and sealing rings, cooperating with the sealing members of the rotor and connected to the fixed guide vane rings, are cooled. Cooling air is supplied through the rotor. The guide vane rings attain a considerably higher temperature than the sealing rings. To prevent great thermal stresses due to different expansion, the sealing rings are movably connected to the guide vane rings. The sealing rings can be connected to a guide vane with radial pins in the guide vanes, which pins project into openings in the sealing rings. The friction between these pins and the sealaing rings may lead to the geometrical axis of the sealing rings being displaced relative to the geometrical axis of the rotor. The resultant eccentricity entails damage to the sealing members on the ring or the rotor, as well as axial leakage resulting in hot combustion gases passing the guide vane ring through gaps formed. A harmful heating of the rotor is obtained.